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Velocity of sound in liquid oxygen and liquid nitrogen as a function of temperature and pressure
Physica 28 861-870
Van Itterbeek, A. Van Dael, W. 1962
VELOCITY NITROGEN
OF SOUND IN LIQUID OXYGEN AND LIQUID AS A FUNCTION OF TEMPERATURE AND PRESSURE
by A. VAN Instituut (Research
ITTERBEEK
voor Lage Temperaturen
and
en Technische
W. VAN Fysika,
DAEL
Leuven
with the financial assistence of the “Instituut tot Aanmoediging pelijk Onderzoek in Nijverheid en Landbouw”).
(Belgi&). van het Wetenschap-
synopsis Measurements are reported on the velocity of ultrasonic pulses in liquid oxygen and liquid nitrogen between 64 and 91’K. The pressure range is limited at the lower side by the vapour pressure line and at the other side by the melting curve, so far it does not exceed a maximum of 1000 kg cm-s.
1. Introduction. Measurements on the velocity of sound W in liquefied gases are very useful in order to extend the existing experimental data on the thermodynamical properties. Moreover this kind of measurements can give us some information about the molecular structure of the liquid. For these reasons we have extended at present our previous work on ultrasonic velocity in liquefied gases up to pressures of 1000 kg cm-21) 2). In the present paper we communicate some definitive experimental results. The calculation of some derived thermodynamical properties together with a comparison with some predictions following from different liquid models will follow later on. 2. Method and apfiaratm. A pulse-echo technique is used at a frequency of 1.1 MHz. Two discs of bariumtitanate are separated by a tube of invar steel filled up with the liquid under investigation. An electrical pulse Pi of 20 psec duration is fed to the first disc A : a sound pulse travels through the liquid and reaches the second disc B after a time-lag t. After reflection on B the echo of Pi arrives at A after 2t. At this moment a new electrical pulse Ps is applied to A - Ps and the twofold reflected PI arrive at the same moment at B. The two signals will add together; if the time 2t equals an integer multiple of the period of the carrier wave, they will intensify each other by interference. The electrical block-scheme of the apparatus is represented in fig. 1. A measurement of the velocity is carried out in the following way. On the -
861 -
862
A. VAN
screen of the oscilloscope
ITTERBEEK
AND W. VAN
DAEL
one regards the signal produced by the transducer
B. The audio-frequent repetition frequency of the pulses is adjusted so that all the ethos, generated by subsequent pulses and arriving in a period 2t, coincide. At this moment the repetition velocity of sound follows directly from W = $
period equals the time 2t. The
= 2Lf,
fr means the repetition frequency of the driving pulse, L is the distance between the two transducers. The length of the resonator is 8.010 cm at 20°C it is made of Nilo 36, a low expansion alloy for which we have used as mean thermal expansion coefficient 1.5 x 10-S deg-1. The value of f,. is of the order of 5 kc and is measured by an electronic counter. The accuracy of this value is only limited by the sharpness of the coincidence of the ethos on the screen. Best results are obtained by adapting at each measurement the carrier frequency, as described above, so that interference occurs. The enveloping pulse has then a maximum amplitude and in the rising wall of the pulse there appear a few sinus tops.
L_r Fig.
sEope r I
1. Block-scheme.
The acoustical system is enclosed in a self-tighting high pressure bomb made of beryllium copper. It is essentially the same as already described in a previous papers). A platinum resistance thermometer is fixed at the outside of the bomb. A chromel-alumel thermocouple controls possible temperature gradients through the wall. After each change in pressure the couple indicates when temperature equilibrium is reached. There is no indication that there would persist a residual temperature difference between the inside of the bomb and the bath. So we have taken the temperature of the resistance thermometer as being valid also in the liquid under investigation. We used industrial gas cylinders with a purity warranted by the manufacturer (Sogaz-Brussels) as better than 99.8% for nitrogen and better than 98.9% for oxygen. The high pressure is obtained by a thermal compressor acting between liquid air and room temperature, or by a 1000 atm
VELOCITY
OF SOUND
IN LIQUID
02
AND
863
N2
mechanical, oil lubricated, pump. (A. Ho f er, Mulheim Germany). A 1000 kg cm-s Heise Bourdon gauge permits pressure readings with an accuracy of 1 kg cm-s. The pressure influence on the length of the acoustical resonator is neglected. 3. Results.
A. Liquid
oxygen
and nitrogen
in equilibrium
with
their saturated vapour. Although they are the latest in chronological order we will firstly mention our results obtained on the vapour pressure line. These measurements were undertaken in the purpose to eliminate a certain discrepancy which appeared when our high pressure velocity isotherms are extrapolated down to the equilibrium vapour pressure and compared with the existing data. Figures 2 and 3 show the present results in liquid oxygen and liquid nitrogen compared with earlier data of Liepmann and VarrItterbeek, De Bock and Verhaegens)d). The scattering of the results is considerably reduced; the internal consistency of this method seems to be much better than that of the earlier investigations carried out by an optical and an interferometric method. The value of the velocity agrees quite well, at least at the normal boiling point. At lower temperatures a slight curvature appears which was masqued before by the scattering of the results. We believe that this must be attributed partly to the difficulties arising in obtaining a well defined temperature in the measuring cell, going out from the vapour pressure of the surrounding bath. The numerical values of the actual results are collected in table I and table II. These measurements are carried out in the way as described already. The temperature is obtained by reducing the vapour pressure of the bath TABLE Velocity
I-
of sound in liquid
oxygen
Series I
W
T OK
i
m set-1 904.6
90.40 88.97
917.3 929.6
87.48 86.04
I
in equilibrium
WC,lC -
Wer,
T
m set-1
OK
-0.2
90.82
-0.4
89.01 87.45
- 0.4 -0.4
with its own vapour
pressure
Series II
I
-
I-
I
W m set-l 901.4 916.6
Woa1e-
m set-’ +0.1 -0.1
929.4
0.0
940.9 953.9
0.0 -0.1 -0.1
84.45
941.3 954.2
83.07
965.1
- 0.2
83.08
964.9
81.39
978.2
f0.2
81.45
977.9
0.0
79.83 78.41 76.95 75.44
990.4 1002.2 1013.3 1025.3
+ 0.3 - 0.3
79.80 78.39 76.84 75.21
990.9 1001.7 1014.2 1026.7 1035.5
0.0 +0.3
74.11 71.74 69.9 1 66.57
-
-0.4
1035.8
0.0 -0.2 - 0.4
1053.9 1066.a 1092.8
-0.4 -0.5 -0.5
86.03 84.45
74.10 72.60 71.36 68.34
1046.9 1056.6 1079.0
wexp
0.0 f0.1 -0.1 0.0 - 0.2 +0.1
1
864
A. VAN ITTERBEEK
AND W. VAN DAEL
--
TABLE II Velocity of sound in liquid nitrogen in equilibrium with its own vapour pressure T
OK 90.74 88.22 86.45 84.55 82.70 80.72 78.64 76.94 75.44 73.21 71.48 70.07 69.03
I
-
W m 93-l
714.5 743.4 762.2 781.9 801.4 821.6 842.8 859.5 874.2 896.3 912.7 925.9 935.2
Weale -
WC-x,
m set-1
+ 0.6 -0.6 - 0.4 +0.1 0.0 +0.2 0.0 + 0.3 + 0.3 -0.2 -0.2 -0.1 +0.2
m set-’ 1100
I\B, al
W
a,
\ 5
Fig. 2. Velocity
3n
92; 5-K
-T with its vapour pressure.
of sound in liquid oxygen in equilibrium 0 Present results; Q A.van Itterbeek, A. de Bock, L. Verhaegen; H. W. Liepmann. 0
filled with liquid oxygen. In order to control the temperature equilibrium we have performed also a set of measurements in liquid oxygen after the bottom of the high pressure vessel was removed (series I). As can be seen in table I there is no systematic difference between the two sets of measure-
VELOCITY
ments carried
OF SOUND
out in a different
portant temperature confirmed moreover
IN LIQUID
02
AND
way. So we conclude
865
N2
that there is no im-
gradient through the metal wall. This by the readings of the thermocouple.
conclusion
is
-
Fig. 3. Velocity of 0 o o
sound in liquid nitrogen in equilibrium with its vapour pressure. Present results; A. van Itterbeek, A. de Rock, L. Verhaegen; H. W. Liepmann
The experimental results can be described by the following valid in the temperature range from 68 to 91°K. For liquid oxygen W =
1140.2 -
7.16a (T -
60) -
0.0186 (T -
60)s.
8.46s (T -
60) -
0.042s (T -
60)s.
equations,
For liquid nitrogen W = 1015.3 -
The deviation of these curves from the experimental points is also indicated in table I and table II as Wcarc - Wexp. B. Liquid oxygen and nitrogen under high pressure. The results of measurements as a function of pressure at constant temperature are collected in tables III and IV.
866
A. VAN
ITTERBEEK
AND
TABLE Velocity
of sound in liquid
VAN
DAEL
A
oxygen’ as a function
of pressure
73.49 OK
67.5s “K P kg cm-s
III
W.
W m set-’
77.73 “K W
fi kg cm-s
m set-1
P kg cm-s
W m set-’
913 871
1330.8 1321.7
916 882
1303.8 1297.2
940
a48 799
1317.2 1306.6
a48 805
1289.0 1279.6
a49
755
1296.7
752
1266.5
a04 756
703 654
1285.2 1273.7
702 651
1255.0 1241.7
702 648
1232.8
606 553
1262.3 1249.4
601 551
1229.4 1217.0
604 552
1206.7 i 194.8
1289.1 1282.2
a99
1268.9 1258.5 :246.0 1219.6
501
1236.3
500
1203.8
503
I 180.5
450 398
1223.3 1210.0
451 401
I 189.9 1175.5
451 404
1166.8 1152.1
351
1197.4
353
1160.4
355
1137.3
301
i 182.5
303
1145.7
302
1120.9
250
1167.6
253
251
1104.0
202
1153.5
202
i 130.8 1114.7
200
1086.7
150
1137.9
152
1098.0
152
1068.1
99 53
1120.9 1105.6
102 51
1080. I 1062.7
101 49
1050.4 1028.8
4
1087.9
4
1043.0
2
1009.4
0.04 *
1085.1
0.11 *
1040.5
0.22 *
1007.3
TABLE Continuation 83.8s OK
of table
IIIA 90.4n “K
I
9
W
kg cm-s
m set-1
921
1257.2
a97 a51
1251.8 1241.1
797
1226.7 1217.1
756
IIIB
kg cm-s
W m set-l
930
1229.2
904 871
1222.7
a35 802
1205.7 1197.6
754
I 183.7 1170.5 1156.0
1214.8
700 652
1189.9
703 653
603
1176.1
602
1140.9
553 503 454
1160.6 1145.2
555 502 454
1126.1 1109.6
405 349
ii
15.8 1097.9
400 351
303
1082.9
253 200 153 106,
1064.0 1044.8 1026.9 1006.9
303 251
59 2 0.51 *
1202.4
P
1131.2
987.8 959.8 958.8
203 154 103 65 2 1.06 *
1093.9 1076.5 1058.7 1041.9 1021.1 1001.9 980.3 957.1 939.8 906.7 905.0
VELOCITY
OF SOUND
IN LIQUID
TABLE Velocity
of sound
in liquid
64.41 “K P kg cm-s
’
P kg cm-s
1020.7 1007.3 990.4 982.5 978.2
536 497 440 421 382 342 299 249 201 150 98 49 22 4 0.65 *
1163,3 1149.0 1127.6 1119.4 1102.9 1085.3 1064.9 1041.0 1016.4 987.9 957.2 924.9 907.1 894.0 892.4
as a function
of pressure
1056.7 1047.9 1034.5 1019.9 1001.4 980.9
a
965.8
3 0.22 *
963.8 960.5
1 kg zrn::“i ‘1 zc-l 78.5 775 755 744 728 717 698 677 652 604 546 502 448
409 350 303 251 201 151 98 50 29 11 1.09 *
69.50 “K W m set-1
178 156 129 101 69 32
Continuation
zc-I
867
Ns
IVA
nitrogen
TABLE
’ 73.6j ‘1 kg cm-s
AND
66.2s “K
W m set-1
72 48 20 4 0.16 *
02
1229.8 1226.8 1220.4 1217.5 1211.9 1208.7 1200.8 1194.1 1184.8 1169.1 1145.7 1128.7 1106.8 1089.5 1060.4 1039.1 1014.6 986.0 956.9 923.1 888.9 874.0 858.2 851.4
I
P kg cm-a
I
334 310 278 241 199 153 99 52 18 3 0.36 *
W m set-1 1106.7 1096.6 1081.9 1065.2 1044.4 1020.9 990.8
962.2 942.0 932.3 931.1
IV B of table
IV A
1 kg I:‘i 984 922 882 781 695 579 492 394 302 198 149 94 55 24 19 12 2.04 *
‘1 Lc-l 1262.7 1247.4 1234.6 1201.1 1171.2 1126.9 1091.0 1046.4 1000.4 940.9 907.7 868.1 837.6 809.0 806.0 798.2 790.9
1 kg -‘:“i 989 948 a90 al4 756 688 593 500 393 299 195 95 70 35 5 3.82 *
‘1 EC-1 1239.4 1227.1 1207.2 1181.9 1161.9 1135.4 1097.4 1058.1 1006.9 956.2 889.3 810.0 786.6 751.6 718.3 717.8
The graphical representation in figures 4 and 5 shows a pronouncd curvature at higher pressures. The triangles at the low pressure side of the isotherms, corresponding with the tabulated values marked with an asterisk, are calculated using the equations (1) and (2). The reliability of both sets of measurements seems to be quite satisfactory.
868
A. VAN
ITTERBEEK
AND W. VAN
DAEL
For liquid oxygen the pressure along the melting curve increases very sharply, a melting pressure of 1000 kg cm-s is already reached at 64.8”K. For liquid nitrogen this same melting pressure corresponds with a temperature of 82.5”K. A dotted line is drawn in fig. 5 through the velocity values at the melting pressure for different temperatures. In all cases there are measuring points lying above this dotted line without the appearance of any discontinuity. All these values correspond to the liquid in a metastable equilibrium.
1 _ i
mser’ 1300
200
Fig. 4. Velocity
400
of second
in liquid
b (0
1
106 IOkgcm-2
600
oxygen
as a function
of pressure.
Previous measurements of the same kind but at lower pressures were made in 1960 by Dobbs and Finegold (up to 135 atm) and by Van Itterbeek and Van D ael in 1958 (75 kg cm-s) and in 1961 (200 kg cm-s) 5) 1) 2). The pressure dependence in all these measurements agrees very well with the present results. It must be emphasized that the calculated most probable curves (table V) have a validity strictly limited to the lower pressure range. However, the absolute values of the velocity show a certain discrepancy at the lowest pressures. The results of Dobbs and Finegold are systematically 0.5% to 1% lower. Our 1958 data were measured with the variable path interferometer method. The accuracy was not so good as in the present series; moreover,
869
VELOCITY OF SOUND IN LIQUID 02 AND Ns
we have drawn the most probable
straight line through
points which in
reality lie on a curve with a negative term in ps. This explains why the Wc values are too high in this first series compared with the other results. In our preliminary results of 1961 we have determined the temperature from vapour pressure readings ; the later experiments have shown the inaccuracy introduced by this method. There may persist a temperature uncertainty which has had no evident influence at 9O.l”K but which explains that the velocities at 77.4 and 87.3”K are a few parts in a thousand lower than the present results. msec-’
i 1200
I
Fig. 5. Velocity of second in liquid nitrogen as a function of pressure.
Finally, making use of an electronic computer we have calculated the equation representing the velocity of sound as a function of pressure
870
VELOCITY
(table VI). Th e velocity
OF SOUND
IN LIQUID
08
AND
Nz
has to be taken in m set-1 and the pressure in kg
cm-2. TABLE Constants
of the equation
+ Bps representing
lv = WO + A, function
Van
Itterbeek
Van
Dael
Dobbs,
(1)
WO mjsec
NZ
90.3 90.2 90.1
1 /
725.0
A
m;;c
Finegold
1
77.4
857.4
0.716
90.3
902.9
0.557
77.3
1007.3
0.449
A
in the
equation
Itterbeek
Van
Dael
(2)
j
104B
m,i,
1
A
/
1~ B
717.4
1.164
- 13.7
1.134
-16.1
744.1
1.109
- 13.4
849.2
0.848
-
851.9
0.804
-
8.9
6.2
VI
W = Wo + Ap + L?pa + Cp3 + Dp4 valid or to 1000 kaicms
A
up to the
melting
_
103 B
10s c
lo9 D
90.50 83.7s
713.4
1.1288
- 1.3771
1.2096
-0.4328
788.0
0.9479
- 1.0585
77.7s
850.3
0.8183
- 0.3685 - 0.4244
73.60
891.3
0.7289
- 0.8684 - 0.6658
0.9579 0.8940 0.7314
- 0.4873
90.40
905.1 958.9
0.5477 0.493 1
-0.4124
83.8s 77.7s
1007.9 1041.4
0.4395
-0.2641
0.4505
- 0.2500
1085.9
0.3709
-0.2016
67.5s
1 I
200 kg cm-e
743.5
m set-i
73.43
i
Van
- 16.3
wo
T OK
02
(5)
1.207
pressure
N2
as a
712.8
TABLE Constants
of sound
I
1.078
87.3 02
the velocity
of uressure
135 atm gauge
75 kg cm-s “K
V
-
- 0.3727
This research has been carried out as a part of a research program in collaboration with the “Institut Belge des Hautes Pressions” directed by Dr. L. Deffet. Received
16-4-62 KEFERENCES
1)
Van Itterbeek, 295-306.
2)
Van
Itterbeek,
A. and Van A. and Van
Dael, Dael,
W.,
Bull.
Inst.
W., Cryogenics
int. du Froid,
Suppl.,
1 (1961) 4, 226.
H. W., Helvetica Phys. Acta II, 9 (1936) 507; I1 (1935) 381. 3) Liepmann, A. and De Bock, A., Physica XIV (1948) 8, 542. 4) Van Itterbeek, E. R. and Finegold, L., J. acoust. Sot. Amer. 52 (1960) 10, 1215. 5) Dobbs,
Annexe
1-1958,
Van Itterbeek, A. Van Dael, W. 1962
VELOCITY NITROGEN
OF SOUND IN LIQUID OXYGEN AND LIQUID AS A FUNCTION OF TEMPERATURE AND PRESSURE
by A. VAN Instituut (Research
ITTERBEEK
voor Lage Temperaturen
and
en Technische
W. VAN Fysika,
DAEL
Leuven
with the financial assistence of the “Instituut tot Aanmoediging pelijk Onderzoek in Nijverheid en Landbouw”).
(Belgi&). van het Wetenschap-
synopsis Measurements are reported on the velocity of ultrasonic pulses in liquid oxygen and liquid nitrogen between 64 and 91’K. The pressure range is limited at the lower side by the vapour pressure line and at the other side by the melting curve, so far it does not exceed a maximum of 1000 kg cm-s.
1. Introduction. Measurements on the velocity of sound W in liquefied gases are very useful in order to extend the existing experimental data on the thermodynamical properties. Moreover this kind of measurements can give us some information about the molecular structure of the liquid. For these reasons we have extended at present our previous work on ultrasonic velocity in liquefied gases up to pressures of 1000 kg cm-21) 2). In the present paper we communicate some definitive experimental results. The calculation of some derived thermodynamical properties together with a comparison with some predictions following from different liquid models will follow later on. 2. Method and apfiaratm. A pulse-echo technique is used at a frequency of 1.1 MHz. Two discs of bariumtitanate are separated by a tube of invar steel filled up with the liquid under investigation. An electrical pulse Pi of 20 psec duration is fed to the first disc A : a sound pulse travels through the liquid and reaches the second disc B after a time-lag t. After reflection on B the echo of Pi arrives at A after 2t. At this moment a new electrical pulse Ps is applied to A - Ps and the twofold reflected PI arrive at the same moment at B. The two signals will add together; if the time 2t equals an integer multiple of the period of the carrier wave, they will intensify each other by interference. The electrical block-scheme of the apparatus is represented in fig. 1. A measurement of the velocity is carried out in the following way. On the -
861 -
862
A. VAN
screen of the oscilloscope
ITTERBEEK
AND W. VAN
DAEL
one regards the signal produced by the transducer
B. The audio-frequent repetition frequency of the pulses is adjusted so that all the ethos, generated by subsequent pulses and arriving in a period 2t, coincide. At this moment the repetition velocity of sound follows directly from W = $
period equals the time 2t. The
= 2Lf,
fr means the repetition frequency of the driving pulse, L is the distance between the two transducers. The length of the resonator is 8.010 cm at 20°C it is made of Nilo 36, a low expansion alloy for which we have used as mean thermal expansion coefficient 1.5 x 10-S deg-1. The value of f,. is of the order of 5 kc and is measured by an electronic counter. The accuracy of this value is only limited by the sharpness of the coincidence of the ethos on the screen. Best results are obtained by adapting at each measurement the carrier frequency, as described above, so that interference occurs. The enveloping pulse has then a maximum amplitude and in the rising wall of the pulse there appear a few sinus tops.
L_r Fig.
sEope r I
1. Block-scheme.
The acoustical system is enclosed in a self-tighting high pressure bomb made of beryllium copper. It is essentially the same as already described in a previous papers). A platinum resistance thermometer is fixed at the outside of the bomb. A chromel-alumel thermocouple controls possible temperature gradients through the wall. After each change in pressure the couple indicates when temperature equilibrium is reached. There is no indication that there would persist a residual temperature difference between the inside of the bomb and the bath. So we have taken the temperature of the resistance thermometer as being valid also in the liquid under investigation. We used industrial gas cylinders with a purity warranted by the manufacturer (Sogaz-Brussels) as better than 99.8% for nitrogen and better than 98.9% for oxygen. The high pressure is obtained by a thermal compressor acting between liquid air and room temperature, or by a 1000 atm
VELOCITY
OF SOUND
IN LIQUID
02
AND
863
N2
mechanical, oil lubricated, pump. (A. Ho f er, Mulheim Germany). A 1000 kg cm-s Heise Bourdon gauge permits pressure readings with an accuracy of 1 kg cm-s. The pressure influence on the length of the acoustical resonator is neglected. 3. Results.
A. Liquid
oxygen
and nitrogen
in equilibrium
with
their saturated vapour. Although they are the latest in chronological order we will firstly mention our results obtained on the vapour pressure line. These measurements were undertaken in the purpose to eliminate a certain discrepancy which appeared when our high pressure velocity isotherms are extrapolated down to the equilibrium vapour pressure and compared with the existing data. Figures 2 and 3 show the present results in liquid oxygen and liquid nitrogen compared with earlier data of Liepmann and VarrItterbeek, De Bock and Verhaegens)d). The scattering of the results is considerably reduced; the internal consistency of this method seems to be much better than that of the earlier investigations carried out by an optical and an interferometric method. The value of the velocity agrees quite well, at least at the normal boiling point. At lower temperatures a slight curvature appears which was masqued before by the scattering of the results. We believe that this must be attributed partly to the difficulties arising in obtaining a well defined temperature in the measuring cell, going out from the vapour pressure of the surrounding bath. The numerical values of the actual results are collected in table I and table II. These measurements are carried out in the way as described already. The temperature is obtained by reducing the vapour pressure of the bath TABLE Velocity
I-
of sound in liquid
oxygen
Series I
W
T OK
i
m set-1 904.6
90.40 88.97
917.3 929.6
87.48 86.04
I
in equilibrium
WC,lC -
Wer,
T
m set-1
OK
-0.2
90.82
-0.4
89.01 87.45
- 0.4 -0.4
with its own vapour
pressure
Series II
I
-
I-
I
W m set-l 901.4 916.6
Woa1e-
m set-’ +0.1 -0.1
929.4
0.0
940.9 953.9
0.0 -0.1 -0.1
84.45
941.3 954.2
83.07
965.1
- 0.2
83.08
964.9
81.39
978.2
f0.2
81.45
977.9
0.0
79.83 78.41 76.95 75.44
990.4 1002.2 1013.3 1025.3
+ 0.3 - 0.3
79.80 78.39 76.84 75.21
990.9 1001.7 1014.2 1026.7 1035.5
0.0 +0.3
74.11 71.74 69.9 1 66.57
-
-0.4
1035.8
0.0 -0.2 - 0.4
1053.9 1066.a 1092.8
-0.4 -0.5 -0.5
86.03 84.45
74.10 72.60 71.36 68.34
1046.9 1056.6 1079.0
wexp
0.0 f0.1 -0.1 0.0 - 0.2 +0.1
1
864
A. VAN ITTERBEEK
AND W. VAN DAEL
--
TABLE II Velocity of sound in liquid nitrogen in equilibrium with its own vapour pressure T
OK 90.74 88.22 86.45 84.55 82.70 80.72 78.64 76.94 75.44 73.21 71.48 70.07 69.03
I
-
W m 93-l
714.5 743.4 762.2 781.9 801.4 821.6 842.8 859.5 874.2 896.3 912.7 925.9 935.2
Weale -
WC-x,
m set-1
+ 0.6 -0.6 - 0.4 +0.1 0.0 +0.2 0.0 + 0.3 + 0.3 -0.2 -0.2 -0.1 +0.2
m set-’ 1100
I\B, al
W
a,
\ 5
Fig. 2. Velocity
3n
92; 5-K
-T with its vapour pressure.
of sound in liquid oxygen in equilibrium 0 Present results; Q A.van Itterbeek, A. de Bock, L. Verhaegen; H. W. Liepmann. 0
filled with liquid oxygen. In order to control the temperature equilibrium we have performed also a set of measurements in liquid oxygen after the bottom of the high pressure vessel was removed (series I). As can be seen in table I there is no systematic difference between the two sets of measure-
VELOCITY
ments carried
OF SOUND
out in a different
portant temperature confirmed moreover
IN LIQUID
02
AND
way. So we conclude
865
N2
that there is no im-
gradient through the metal wall. This by the readings of the thermocouple.
conclusion
is
-
Fig. 3. Velocity of 0 o o
sound in liquid nitrogen in equilibrium with its vapour pressure. Present results; A. van Itterbeek, A. de Rock, L. Verhaegen; H. W. Liepmann
The experimental results can be described by the following valid in the temperature range from 68 to 91°K. For liquid oxygen W =
1140.2 -
7.16a (T -
60) -
0.0186 (T -
60)s.
8.46s (T -
60) -
0.042s (T -
60)s.
equations,
For liquid nitrogen W = 1015.3 -
The deviation of these curves from the experimental points is also indicated in table I and table II as Wcarc - Wexp. B. Liquid oxygen and nitrogen under high pressure. The results of measurements as a function of pressure at constant temperature are collected in tables III and IV.
866
A. VAN
ITTERBEEK
AND
TABLE Velocity
of sound in liquid
VAN
DAEL
A
oxygen’ as a function
of pressure
73.49 OK
67.5s “K P kg cm-s
III
W.
W m set-’
77.73 “K W
fi kg cm-s
m set-1
P kg cm-s
W m set-’
913 871
1330.8 1321.7
916 882
1303.8 1297.2
940
a48 799
1317.2 1306.6
a48 805
1289.0 1279.6
a49
755
1296.7
752
1266.5
a04 756
703 654
1285.2 1273.7
702 651
1255.0 1241.7
702 648
1232.8
606 553
1262.3 1249.4
601 551
1229.4 1217.0
604 552
1206.7 i 194.8
1289.1 1282.2
a99
1268.9 1258.5 :246.0 1219.6
501
1236.3
500
1203.8
503
I 180.5
450 398
1223.3 1210.0
451 401
I 189.9 1175.5
451 404
1166.8 1152.1
351
1197.4
353
1160.4
355
1137.3
301
i 182.5
303
1145.7
302
1120.9
250
1167.6
253
251
1104.0
202
1153.5
202
i 130.8 1114.7
200
1086.7
150
1137.9
152
1098.0
152
1068.1
99 53
1120.9 1105.6
102 51
1080. I 1062.7
101 49
1050.4 1028.8
4
1087.9
4
1043.0
2
1009.4
0.04 *
1085.1
0.11 *
1040.5
0.22 *
1007.3
TABLE Continuation 83.8s OK
of table
IIIA 90.4n “K
I
9
W
kg cm-s
m set-1
921
1257.2
a97 a51
1251.8 1241.1
797
1226.7 1217.1
756
IIIB
kg cm-s
W m set-l
930
1229.2
904 871
1222.7
a35 802
1205.7 1197.6
754
I 183.7 1170.5 1156.0
1214.8
700 652
1189.9
703 653
603
1176.1
602
1140.9
553 503 454
1160.6 1145.2
555 502 454
1126.1 1109.6
405 349
ii
15.8 1097.9
400 351
303
1082.9
253 200 153 106,
1064.0 1044.8 1026.9 1006.9
303 251
59 2 0.51 *
1202.4
P
1131.2
987.8 959.8 958.8
203 154 103 65 2 1.06 *
1093.9 1076.5 1058.7 1041.9 1021.1 1001.9 980.3 957.1 939.8 906.7 905.0
VELOCITY
OF SOUND
IN LIQUID
TABLE Velocity
of sound
in liquid
64.41 “K P kg cm-s
’
P kg cm-s
1020.7 1007.3 990.4 982.5 978.2
536 497 440 421 382 342 299 249 201 150 98 49 22 4 0.65 *
1163,3 1149.0 1127.6 1119.4 1102.9 1085.3 1064.9 1041.0 1016.4 987.9 957.2 924.9 907.1 894.0 892.4
as a function
of pressure
1056.7 1047.9 1034.5 1019.9 1001.4 980.9
a
965.8
3 0.22 *
963.8 960.5
1 kg zrn::“i ‘1 zc-l 78.5 775 755 744 728 717 698 677 652 604 546 502 448
409 350 303 251 201 151 98 50 29 11 1.09 *
69.50 “K W m set-1
178 156 129 101 69 32
Continuation
zc-I
867
Ns
IVA
nitrogen
TABLE
’ 73.6j ‘1 kg cm-s
AND
66.2s “K
W m set-1
72 48 20 4 0.16 *
02
1229.8 1226.8 1220.4 1217.5 1211.9 1208.7 1200.8 1194.1 1184.8 1169.1 1145.7 1128.7 1106.8 1089.5 1060.4 1039.1 1014.6 986.0 956.9 923.1 888.9 874.0 858.2 851.4
I
P kg cm-a
I
334 310 278 241 199 153 99 52 18 3 0.36 *
W m set-1 1106.7 1096.6 1081.9 1065.2 1044.4 1020.9 990.8
962.2 942.0 932.3 931.1
IV B of table
IV A
1 kg I:‘i 984 922 882 781 695 579 492 394 302 198 149 94 55 24 19 12 2.04 *
‘1 Lc-l 1262.7 1247.4 1234.6 1201.1 1171.2 1126.9 1091.0 1046.4 1000.4 940.9 907.7 868.1 837.6 809.0 806.0 798.2 790.9
1 kg -‘:“i 989 948 a90 al4 756 688 593 500 393 299 195 95 70 35 5 3.82 *
‘1 EC-1 1239.4 1227.1 1207.2 1181.9 1161.9 1135.4 1097.4 1058.1 1006.9 956.2 889.3 810.0 786.6 751.6 718.3 717.8
The graphical representation in figures 4 and 5 shows a pronouncd curvature at higher pressures. The triangles at the low pressure side of the isotherms, corresponding with the tabulated values marked with an asterisk, are calculated using the equations (1) and (2). The reliability of both sets of measurements seems to be quite satisfactory.
868
A. VAN
ITTERBEEK
AND W. VAN
DAEL
For liquid oxygen the pressure along the melting curve increases very sharply, a melting pressure of 1000 kg cm-s is already reached at 64.8”K. For liquid nitrogen this same melting pressure corresponds with a temperature of 82.5”K. A dotted line is drawn in fig. 5 through the velocity values at the melting pressure for different temperatures. In all cases there are measuring points lying above this dotted line without the appearance of any discontinuity. All these values correspond to the liquid in a metastable equilibrium.
1 _ i
mser’ 1300
200
Fig. 4. Velocity
400
of second
in liquid
b (0
1
106 IOkgcm-2
600
oxygen
as a function
of pressure.
Previous measurements of the same kind but at lower pressures were made in 1960 by Dobbs and Finegold (up to 135 atm) and by Van Itterbeek and Van D ael in 1958 (75 kg cm-s) and in 1961 (200 kg cm-s) 5) 1) 2). The pressure dependence in all these measurements agrees very well with the present results. It must be emphasized that the calculated most probable curves (table V) have a validity strictly limited to the lower pressure range. However, the absolute values of the velocity show a certain discrepancy at the lowest pressures. The results of Dobbs and Finegold are systematically 0.5% to 1% lower. Our 1958 data were measured with the variable path interferometer method. The accuracy was not so good as in the present series; moreover,
869
VELOCITY OF SOUND IN LIQUID 02 AND Ns
we have drawn the most probable
straight line through
points which in
reality lie on a curve with a negative term in ps. This explains why the Wc values are too high in this first series compared with the other results. In our preliminary results of 1961 we have determined the temperature from vapour pressure readings ; the later experiments have shown the inaccuracy introduced by this method. There may persist a temperature uncertainty which has had no evident influence at 9O.l”K but which explains that the velocities at 77.4 and 87.3”K are a few parts in a thousand lower than the present results. msec-’
i 1200
I
Fig. 5. Velocity of second in liquid nitrogen as a function of pressure.
Finally, making use of an electronic computer we have calculated the equation representing the velocity of sound as a function of pressure
870
VELOCITY
(table VI). Th e velocity
OF SOUND
IN LIQUID
08
AND
Nz
has to be taken in m set-1 and the pressure in kg
cm-2. TABLE Constants
of the equation
+ Bps representing
lv = WO + A, function
Van
Itterbeek
Van
Dael
Dobbs,
(1)
WO mjsec
NZ
90.3 90.2 90.1
1 /
725.0
A
m;;c
Finegold
1
77.4
857.4
0.716
90.3
902.9
0.557
77.3
1007.3
0.449
A
in the
equation
Itterbeek
Van
Dael
(2)
j
104B
m,i,
1
A
/
1~ B
717.4
1.164
- 13.7
1.134
-16.1
744.1
1.109
- 13.4
849.2
0.848
-
851.9
0.804
-
8.9
6.2
VI
W = Wo + Ap + L?pa + Cp3 + Dp4 valid or to 1000 kaicms
A
up to the
melting
_
103 B
10s c
lo9 D
90.50 83.7s
713.4
1.1288
- 1.3771
1.2096
-0.4328
788.0
0.9479
- 1.0585
77.7s
850.3
0.8183
- 0.3685 - 0.4244
73.60
891.3
0.7289
- 0.8684 - 0.6658
0.9579 0.8940 0.7314
- 0.4873
90.40
905.1 958.9
0.5477 0.493 1
-0.4124
83.8s 77.7s
1007.9 1041.4
0.4395
-0.2641
0.4505
- 0.2500
1085.9
0.3709
-0.2016
67.5s
1 I
200 kg cm-e
743.5
m set-i
73.43
i
Van
- 16.3
wo
T OK
02
(5)
1.207
pressure
N2
as a
712.8
TABLE Constants
of sound
I
1.078
87.3 02
the velocity
of uressure
135 atm gauge
75 kg cm-s “K
V
-
- 0.3727
This research has been carried out as a part of a research program in collaboration with the “Institut Belge des Hautes Pressions” directed by Dr. L. Deffet. Received
16-4-62 KEFERENCES
1)
Van Itterbeek, 295-306.
2)
Van
Itterbeek,
A. and Van A. and Van
Dael, Dael,
W.,
Bull.
Inst.
W., Cryogenics
int. du Froid,
Suppl.,
1 (1961) 4, 226.
H. W., Helvetica Phys. Acta II, 9 (1936) 507; I1 (1935) 381. 3) Liepmann, A. and De Bock, A., Physica XIV (1948) 8, 542. 4) Van Itterbeek, E. R. and Finegold, L., J. acoust. Sot. Amer. 52 (1960) 10, 1215. 5) Dobbs,
Annexe
1-1958,